ncrease over T years is erT . This latter is properly equated to R0, the Net Reproduction Rate:
vhich provides for the United States in 1966 the equation in r
e26.2r = L2Q5.
Faking natural logarithms of both sides gives
igainst the Canadian r = 0.00716. As was said, the rapid turnover of the Jnited States population partly offsets its lower NRR.
We saw that the Net Reproduction Rate is slightly more affected by a small decline of the birth rate at age 15 to 19 than it is by the same decline at 40 to 44; after all, some of the women alive at the younger age die before the older, and for them the number of children they would have had at 40 to 44 does not count. The younger women are also more important because their births imply less time between generations. Furthermore, in a rapidly increasing population there can be twice as many women at age 20 than at age 40, making fertility of younger women of greater importance. All these facts are implicitly incorporated in the intrinsic rate r.
Change in the Intrinsic Rate r Consequent upon Change in an Age-Specific Birth Rate
The intrinsic rate r summarizes a regime of mortality and fertility; it does so by telling us the ultimate rate of increase of any population in which that regime applies. To know how r is affected by a change AF^ in the age-specific fertility rate from age jc to x + 4 at last birthday is one way of extracting the significance for the future of AFX. It is easily shown (4, p. 352) that the corresponding modification of r is in general
e-r(y+VA) I AF
A,_____________5 y y
where t6 is the mean age of childbearing in the stable population.
From this result it follows that the effect on r of a reduction in the Fy when v is 15 to 19 is verv much more than the effect of a reduction when y isomparison of Canada and the United States for 1967 shows that the Net Reproduction Rate does not tell the whole story of replacement. Canada's NRR was slightly higher than that of the United States, 1.216 against 1.205. The Canadian girl child just born could expect to bear slightly more girl children than the United States girl child at 1967 rates. But the Canadian would marry older and have her children later within marriage; her length of generation— a measure something like the average age of childbearing-was 27.3 years against the United States 26.2 years. This means a more rapid turnover of generations in the United States.